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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 89 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.5x + 3y = 1 and 3x + 4y = 16 →
  2. 2.3x + 5y = 58 and 2x + 4y = 44 →
  3. 3.4x + y = 44 and x + 4y = 41 →
  4. 4.2x + 5y = 31 and 5x − 6y = −15 →
  5. 5.x + 2y = −4 and 4x + 2y = −22 →
  6. 6.4x + 4y = 44 and 4x + 5y = 53 →
  7. 7.2x + y = 12 and x + 6y = 39 →
  8. 8.3x + 3y = 51 and 3x + y = 35 →
  9. 9.x + 2y = 10 and 2x + y = −7 →
  10. 10.6x − 4y = −52 and 4x + 2y = −30 →
  11. 11.2x − 6y = −30 and 6x + 3y = 57 →
  12. 12.x − 3y = −6 and 5x − 4y = 25 →
  13. 13.2x − 4y = −20 and 5x − y = 31 →
  14. 14.3x − 2y = 36 and 6x + 5y = 18 →
  15. 15.2x + 5y = −50 and 5x − 6y = 23 →
  16. 16.5x − 5y = 0 and 2x + 6y = 32 →
  17. 17.6x + 4y = −2 and 4x + 6y = 2 →
  18. 18.6x + 5y = −40 and 4x + 3y = −26 →
  19. 19.5x + 3y = 51 and 3x + 5y = 53 →
  20. 20.3x + 3y = 42 and 6x + 2y = 60 →
  21. 21.4x + 2y = 40 and 5x − 2y = 14 →
  22. 22.2x − 5y = 38 and 2x − y = 14 →
  23. 23.4x + 8y = 0 and 8x + 4y = 36 →
  24. 24.5x + 3y = 28 and 3x + 5y = 20 →
  25. 25.x + 2y = −5 and 5x − 5y = 20 →
  26. 26.2x + 6y = 0 and 6x + 2y = −16 →
  27. 27.6x − y = −39 and 2x − 3y = −37 →
  28. 28.2x + 8y = 42 and 8x + 2y = 48 →
  29. 29.x − 3y = 11 and 2x + 3y = −14 →
  30. 30.6x + 2y = 30 and 2x + 6y = −6 →
  31. 31.4x − 3y = −2 and 4x + 2y = −32 →
  32. 32.3x + 6y = 24 and 3x + 4y = 12 →
  33. 33.2x + 5y = 23 and 2x + 3y = 21 →
  34. 34.6x − 3y = 0 and 3x − 4y = −15 →
  35. 35.4x + 9y = 51 and 9x + 4y = 66 →
  36. 36.9x + 6y = −45 and 6x + 9y = 0 →
  37. 37.4x − 4y = −12 and 3x + y = 11 →
  38. 38.5x + 2y = 59 and 2x + 4y = 46 →
  39. 39.x + 6y = 4 and 6x + y = −11 →
  40. 40.2x − 6y = 20 and 3x + 3y = −42 →

Answer key

  1. x = −4, y = 7
  2. x = 6, y = 8
  3. x = 9, y = 8
  4. x = 3, y = 5
  5. x = −6, y = 1
  6. x = 2, y = 9
  7. x = 3, y = 6
  8. x = 9, y = 8
  9. x = −8, y = 9
  10. x = −8, y = 1
  11. x = 6, y = 7
  12. x = 9, y = 5
  13. x = 8, y = 9
  14. x = 8, y = −6
  15. x = −5, y = −8
  16. x = 4, y = 4
  17. x = −1, y = 1
  18. x = −5, y = −2
  19. x = 6, y = 7
  20. x = 8, y = 6
  21. x = 6, y = 8
  22. x = 4, y = −6
  23. x = 6, y = −3
  24. x = 5, y = 1
  25. x = 1, y = −3
  26. x = −3, y = 1
  27. x = −5, y = 9
  28. x = 5, y = 4
  29. x = −1, y = −4
  30. x = 6, y = −3
  31. x = −5, y = −6
  32. x = −4, y = 6
  33. x = 9, y = 1
  34. x = 3, y = 6
  35. x = 6, y = 3
  36. x = −9, y = 6
  37. x = 2, y = 5
  38. x = 9, y = 7
  39. x = −2, y = 1
  40. x = −8, y = −6

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